💿🐜 Antkeeper source code
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79 lines
2.1 KiB
79 lines
2.1 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_PHYSICS_ORBIT_KEPLER_HPP
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#define ANTKEEPER_PHYSICS_ORBIT_KEPLER_HPP
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#include <cmath>
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namespace physics {
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namespace orbit {
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/**
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* Iteratively solves Kepler's equation for eccentric anomaly (E).
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*
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* @param ec Eccentricity (e).
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* @param ma Mean anomaly (M).
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* @param iterations Maximum number of iterations.
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* @param tolerance Solution error tolerance.
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* @return Eccentric anomaly (E).
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*/
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template <class T>
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T kepler_ea(T ec, T ma, std::size_t iterations, T tolerance = T(0));
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/**
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* Solves Kepler's equation for mean anomaly (M).
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*
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* @param ec Eccentricity (e).
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* @param ea Eccentric anomaly (E).
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* @return Mean anomaly (M).
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*/
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template <class T>
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T kepler_ma(T ec, T ea);
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template <class T>
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T kepler_ea(T ec, T ma, std::size_t iterations, T tolerance)
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{
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// Approximate eccentric anomaly, E
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T ea0 = ma + ec * std::sin(ma) * (T(1.0) + ec * std::cos(ma));
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// Iteratively converge E0 and E1
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for (std::size_t i = 0; i < iterations; ++i)
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{
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const T ea1 = ea0 - (ea0 - ec * std::sin(ea0) - ma) / (T(1.0) - ec * std::cos(ea0));
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const T error = std::abs(ea1 - ea0);
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ea0 = ea1;
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if (error < tolerance)
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break;
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}
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return ea0;
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}
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template <class T>
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T kepler_ma(T ec, T ea)
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{
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return ea - ec * std::sin(ea);
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}
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} // namespace orbit
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} // namespace physics
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#endif // ANTKEEPER_PHYSICS_ORBIT_KEPLER_HPP
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